Is there a standard way to organize methods within a class? [duplicate]

StyleCop enforces some things here:

Within a class, struct, or interface, elements must be positioned in the following order:

• Fields
• Constructors
• Finalizers (Destructors)
• Delegates
• Events
• Enums
• Interfaces
• Properties
• Indexers
• Methods
• Structs
• Classes

Furthermore, elements are ordered by access:

• public
• internal
• protected internal
• protected
• private

As well as a few other rules:

• Contants have to appear before fields
• static elements have to appear before instance elements.

This might be a good baseline to start. As for additional ordering rules, I usually group related methods together.